A
tournament
is a directed graph
T
such that every pair of vertices is connected by an arc. A
feedback vertex set
is a set
S
of vertices in
T
such that
T
−
S
is acyclic. We consider the Feedback Vertex Set problem in tournaments. Here, the input is a tournament
T
and a weight function
w
:
V
(
T
) → N, and the task is to find a feedback vertex set
S
in
T
minimizing
w
(
S
) = ∑
v∈S
w
(
v
). Rounding optimal solutions to the natural LP-relaxation of this problem yields a simple 3-approximation algorithm. This has been improved to 2.5 by Cai et al. [SICOMP 2000], and subsequently to 7/3 by Mnich et al. [ESA 2016]. In this article, we give the first polynomial time factor 2-approximation algorithm for this problem. Assuming the Unique Games Conjecture, this is the best possible approximation ratio achievable in polynomial time.
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem
